(9x+6)(3x)=360x+82

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Solution for (9x+6)(3x)=360x+82 equation:



(9x+6)(3x)=360x+82
We move all terms to the left:
(9x+6)(3x)-(360x+82)=0
We multiply parentheses
27x^2+18x-(360x+82)=0
We get rid of parentheses
27x^2+18x-360x-82=0
We add all the numbers together, and all the variables
27x^2-342x-82=0
a = 27; b = -342; c = -82;
Δ = b2-4ac
Δ = -3422-4·27·(-82)
Δ = 125820
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{125820}=\sqrt{36*3495}=\sqrt{36}*\sqrt{3495}=6\sqrt{3495}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-342)-6\sqrt{3495}}{2*27}=\frac{342-6\sqrt{3495}}{54} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-342)+6\sqrt{3495}}{2*27}=\frac{342+6\sqrt{3495}}{54} $

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